What is the derivative of f(x)=4x^2e^{2x^2+x-1} ?

The derivative of f(x)=4x^2e^{2x^2+x-1} is 4(2xe^{2x^2+x-1}+e^{2x^2+x-1}(4x+1)x^2)

What is the first derivative of f(x)=4x^2e^{2x^2+x-1} ?

The first derivative of f(x)=4x^2e^{2x^2+x-1} is 4(2xe^{2x^2+x-1}+e^{2x^2+x-1}(4x+1)x^2)

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derivative of

f (x) = 4 x^{2} e^{2 x^{2} + x - 1}

4 (2 x e^{2 x^{2} + x - 1} + e^{2 x^{2} + x - 1} (4 x + 1) x^{2})

Solution steps

\frac{d}{d x} (4 x^{2} e^{2 x^{2} + x - 1})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (x^{2} e^{2 x^{2} + x - 1})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = e^{2 x^{2} + x - 1}

= 4 (\frac{d}{d x} (x^{2}) e^{2 x^{2} + x - 1} + \frac{d}{d x} (e^{2 x^{2} + x - 1}) x^{2})

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (e^{2 x^{2} + x - 1}) = e^{2 x^{2} + x - 1} (4 x + 1)

= 4 (2 x e^{2 x^{2} + x - 1} + e^{2 x^{2} + x - 1} (4 x + 1) x^{2})

\int 13 - (\frac{x}{40}) d x

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\int 3 x^{2} + 4 x - 1 d x

\frac{d}{d x} (x y)

What is the derivative of f(x)=4x^2e^{2x^2+x-1} ?
The derivative of f(x)=4x^2e^{2x^2+x-1} is 4(2xe^{2x^2+x-1}+e^{2x^2+x-1}(4x+1)x^2)
What is the first derivative of f(x)=4x^2e^{2x^2+x-1} ?
The first derivative of f(x)=4x^2e^{2x^2+x-1} is 4(2xe^{2x^2+x-1}+e^{2x^2+x-1}(4x+1)x^2)